f(x) = x-5
g(x)= x^3
h(x)= √x^2+1
Write this expession as a composition, using only the functions f,g and h.
√ (x^3 - 5)^2 + 1
Does anyone know how to do this please? I have an exam coming up and I would appreciate it.

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- amistre64

the copy and paste technique tends to cut off the top of the radical. Can you tell us what is spossed to be 'under' the radical?

- amistre64

(h o f o g)(x) is one way to write this thing

- amistre64

h(f(x)) = sqrt. f(x)^2 + 1
f(g(x)) = g(x) - 5
g(x) = x^3
its like nesting functions; you fit them into each other like a set of russian dolls

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## More answers

- anonymous

It is all meant to be under it. I was thinking that was the answer but I don't know how to work it out. Could you please tell me how you got the answer?

- anonymous

Thank you so much for your help. I understand it a lot better now.

- amistre64

i simply used the facts they gave and tore the new equation apart to investigate its inner workings

- amistre64

we had to rip out the 'x' part and re constuct it with the missing pieces

- amistre64

sqrt. ______ ^2 +1 ; h(x) matches the profile , h(f(g(x)))
/||||||||\
_______ - 5 ; f(x) matches the profile, f(g(x))
/|||||||||\
----- ; g(x) matches the profile

- anonymous

Yeah that makes sense thanks.

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